I Don’t Stand a Ghost of Chance With You

The music was composed by Victor Young, with lyrics written by Ned Washington and Bing Crosby. The song is a jazz and pop standard recorded by many different artists.[1][2]

The song was recorded on October 14, 1932 by Bing Crosby in New York. Bing Crosby was accompanied by the ARC Brunswick Studio Orchestra with Lennie Hayton on piano. Two master versions were recorded: B12474-A at 3:12 and B12474-B at 3:18. The recording was released as a 78 single as Brunswick 6454, b/w “Just an Echo in the Valley”, and Columbia DB-2030, b/w “Cabin in the Cotton”, and as a 45, Columbia 39524, b/w “Temptation”.

Bing Crosby performed the song in the 1933 Mack Sennett film short Please in which he starred as Howard Jones [sic] directed by Arvid E. Gillstrom.[4]

1932

Gene Austin with the Dorsey Brothers Orchestra — I haven’t confirmed the date, but according to Second Hand Songs Greta Keller also released a recording in 1932. Jazzstandards.com and Wikipedia indicate that Bing Crosby recorded the song first.

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Bing Crosby — The clip is from the 1933 Paramount musical comedy short titled Please.

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Mildred Bailey — 1939

The video provider says,

In 1939, Mildred Bailey fronted a six-side, mostly blues session as “Mildred Bailey and her Oxford Greys” for Vocalion, which featured a small mixed-race combo of Mary Lou Williams (piano), Floyd Smith (electric guitar), John Williams (bass) and Eddie Dougherty (drums).

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Lionel Hampton and his Orchestra, vocal: Helen Forrest — B-side of the 78 rpm single Dough-Ra-Me (Victor 26696) recorded 17 July 1940

Despite the credit to Hampton and his Orchestra, the label gives the players as follows — Lionel Hampton: vibraharp [vibraphone], Nat King Cole: piano, Wesley Prince: bass, Oscar Moore: guitar, Al Spieldock: drums. In other words, we have Hampton, the original Nat King Cole trio, and Spieldock. Second Hand Songs gives the band name as The Hampton Rhythm Boys.

Lester Young – Live radio Broadast of 21 January 1951 – Lester Young – ts, Jonah Jones-trp, John Lewis – p, Geney Ramey – b, Joe Jones – d. It sounds like it was recorded in a busy club; there are voices chatting away throughout the song.